1. Field of the Invention
The present invention relates generally to a thin metal film interconnect for an integrated circuit, and more particularly to improving the resistance of a thin metal film to electromigration failure when the minimum linewidth of the integrated circuit fabrication process is less than one and one-half times the mean metal grain size of the metal film. Specifically, the invention relates to the use of parallel-connected narrow-width metal film lines to enhance the resistance of interconnections to electromigration failure.
2. Description of the Background Art
Thin metal film power buses in very-large-scale (VLSI) integrated circuits are known to have reliability problems due to mechanical and electrical instability when conducting high current densities. Mechanical stress, for example, results from the mismatch in thermal expansion coefficients between the metal film and the semiconductor substrate. It is known, for example, to improve the mechanical stability of thin metal film power buses by forming in the bus a number of equally-spaced and staggered slots parallel to the direction of current flow in the bus. The slotting permits the metal film to readily expand and contract without cracking and without disengagement from the substrate when the substrate expands and contracts in response to temperature changes.
Electromigration refers to a net motion of atoms due to the passage of electrical current through a metallic conductor. Aluminum-based thin-film metallizations, as widely used to form conductor patterns in silicon integrated circuits, are especially susceptible to failure from electromigration. The passage of a large current density creates a viscous drag on the metal ions, resulting in a diffusion of metal ions and vacancies in opposite direction. Near a point of flux divergence, the vacancies coalesce to form voids, which may cause an open-circuit failure. The metal atoms pile up downstream to form hillocks.
At the temperatures that are relevant to electromigration in thin metal film interconnects for integrated circuits, the dominant transport mechanism is grain-boundary diffusion. The grain-boundary diffusion varies from boundary to boundary according to the relative orientation of adjacent grains. Thin metal films do not usually have a very uniform grain size, and changes in grain size are often found where failures have occurred. Grain boundary triple points are a common cause of atomic flux divergence, and, therefore, voids due to electromigration tend to form at triple points. Failure will occur along the length of a conductor where void formation extends first across the whole width of the conductor.
It has been known for many years that the resistance of a thin-film metal line to electromigration failure is a function of the length and the width of the line. Failures occur randomly among similar samples, and, therefore, electromigration resistance is typically measured by a median failure time, "t.sub.50 ", and a standard deviation, ".sigma.", in the failure time. Long metal lines tend to have short t.sub.50, but also small .sigma., since the probability of a configuration to early failures increases with the line length, and infinitely long lines would have identical distributions of structural configurations (hence equal failure times).
Studies of the width dependence of electromigration lifetimes in aluminum thin-film lines show that for a constant line length, the median failure time t.sub.50 first decreases and then sharply increases as the line width W decreases. The width having the minimum t.sub.50 is a function of the mean grain size D of the metal, with the minimum t.sub.50 occurring at a width W of approximately twice the mean grain size D. The deviation .sigma., however, continually increases as the width W decreases. This behavior can be explained by serial and parallel failure unit models. For lines that are much wider than the mean grain size, there is an abundance of paths for migration parallel to the current flow. Assuming that potential failure sites such as triple-points are uniformly distributed and voids form at the triple-points, it is expected that the median failure time would decrease with decreasing width, because there would be a decreasing availability of paths for current flow around the voids. For lines that are much narrower than the mean grain size, however, the number of potential failure sites such as triple-points per unit length of the line decreases sharply with a decrease in line width. Therefore, there is a sharp increase in the mean failure time t.sub.50 when the line width W decreases below the mean grain size.
When the width of a line is comparable to the mean grain size, the metal line behaves as a serial combination of "N" independent "failure units", so that the length of the line, "L", is related to N by: EQU L=(N)(L.sub.0) (Equation 1)
where L.sub.0 is the length of an independent failure unit. In accordance with this serial failure unit model, as soon as any one of the units fails, the whole line fails. The line cumulative probability of failure, "G(t)", therefore, should be related to the unit probability of failure, "F(t)", by: EQU G(t)=1-(1-F(t)).sup.N (Equation 2)
N is larger, and G(t) is higher, for longer lines. Moreover, there is a "saturation" of lifetime as L increases many times greater than L.sub.0.
The unit probability of failure F(t) typically follows a lognormal function. In this case, the cumulative probability of failure, G(t), becomes the so-called "multi-lognormal" (MLN) cumulative distribution function: EQU G*(t)=1-(1/2[1-erf((ln (t/t'.sub.50))/.sqroot.2.sigma.')]).sup.N(Equation 3)
where t'.sub.50 and .sigma.' are the median and standard deviation of the unit failure probability distribution function F(t). The median lifetime t*.sub.50 of the multi-lognormal probability distribution function F*(t) is given by: EQU t*.sub.50 =t'.sub.50 exp [.sqroot.2.sigma.'erf.sup.-1 (1-2(0.5).sup.1/N)](Equation 4)
A shape factor .sigma.* for the multi-lognormal cumulative distribution function G*(t) can be defined as the least squares lognormal fit through the 16% and 84% points of the multi-lognormal cumulative distribution function. As a function of the lognormal .sigma.' and N, .sigma.* is given by: EQU .sigma.*=.sqroot.2.sigma.'[erf.sup.-1 (1-2(0.16).sup.1/N)-erf.sup.-1 (1-2(0.84).sup.1/N)] (Equation 5)
In addition to the length L.sub.0 of an independent failure unit, there is discussion in the technical literature of other critical lengths related to potential failure sites. E. Kinsborn, "A model for the width dependence of electromigration lifetimes in aluminum thin-film strips." Appl. Phys. Letters, Vol. 36, No. 12, Jun. 15, 1980, pp. 968-970, for example, on pages 969-970, says that mass depletion at a cathode end of a metal line and mass accumulation at the anode end will build stress and concentration gradients between the anode and cathode ends. This gradient (inversely proportional to the line length) will create a reverse mass flow to the one produced by electromigration. For a given temperature and current density, there is a critical length 1.sub.c below which backflow will balance the forward flux. For lines with widths small enough to form segments blocked by single-crystal grains, the time to failure and the failure location will be dependent on the difference between the length of the longest polycrystalline segment in the strip 1.sub.max and the threshold length 1.sub.c. Generally, the stress gradient that produces the reversed atomic flow is built by the migrating atoms responding to the electromigration driving force. These migrating atoms will leave behind a vacancy concentration which will form voids after a certain period. During the time necessary to establish the final stress gradient, the depletion of atoms may be sufficient to cause voids to grow until the conductor line opens. In this event, the sample will fail even for polycrystalline segments shorter than 1.sub.c. The narrower the lines are, the higher probability of early failure, unless the failure structure permits a segmentation having very short lengths, or even a series of single crystals. In this event, the stress gradient will be built instantaneously and the void growth ceases before it reaches its critical size.
J. R. Lloyd and J. Kitchin, "The electromigration failure distribution: The fine-line case," J. App. Phys., Vol. 69, No. 4, Feb. 14, 1991, pp. 2117-2127, on pages 2123 to 2124, discuss the selection of a failure element length for an electromigration failure model. Arguments have been proposed that suggest that the effect of stress gradients produced at locations of inverse flux divergence may be to change the rate of diffusion such that the flux divergence can vanish, eliminating the source as a potential failure site. This viewpoint is consistent with the experimental failure characteristics which suggest that the length of the failure element is larger than the grain size, and may be on the order of tens or hundreds of microns. For the failure model, another choice would be the length of conductor where we are certain that each element could act independently. This would be the so-called "Blech Length" which is the expected distance over which an electromigration-induced stress gradient would be significant, expressed as KT/F, where F is the electromigration driving force. This length is on the order of tens to hundreds of microns.